The complete lecture — every ray diagram builds itself in the live panel on the right as you read. Watch i equal r, slide an object along a concave mirror's axis, bend light at a water surface, and trap a ray inside an optical fibre.
1 — Rectilinear propagation & shadows
In a uniform medium light travels in straight lines — rectilinear propagation. A ray is the straight path light takes; a bundle of rays is a beam.
- Shadows — a point source gives a totally dark umbra; an extended source adds the half-lit penumbra border.
- Eclipses — solar: the Moon's shadow on Earth; lunar: the Earth's shadow on the Moon.
- Pinhole camera — straight rays cross at the hole and form a real, inverted image.
Exam point: shadows, eclipses and the pinhole camera are the three classic proofs of rectilinear propagation.
2 — Laws of reflection
Both angles are measured from the normal, never from the mirror surface.
Laws of reflection1. incident ray, reflected ray & normal lie in one plane
2. ∠i = ∠r — always
Watch the panel: as the incident ray swings from 18° to 68°, the reflected ray copies it exactly. A mirror rotated through θ swings the reflected ray through 2θ.
3 — Plane mirrors & lateral inversion
- Virtual & erect — no light actually goes behind the mirror; the image cannot fall on a screen.
- q = p, same size — image distance equals object distance; magnification 1.
- Lateral inversion — left ↔ right swap; AMBULANCE is mirror-painted so drivers read it correctly in the rear-view mirror.
worked — distance to your image
You stand 1.5 m from a plane mirror.
image 1.5 m behind → you-to-image = 1.5 + 1.5 = 3.0 m
4 — Spherical mirrors & the mirror formula
A concave mirror converges light; a convex mirror diverges it. The focus sits halfway to the centre of curvature: f = R/2. Two rays locate any image: parallel-ray → reflects through F; ray through C → reflects back on itself.
Mirror formula & magnification1/f = 1/p + 1/q · m = q/p
f = R/2 · concave f positive, convex f negative
worked — concave mirror
p = 30 cm, f = 10 cm.
1/q = 1/10 − 1/30 = 2/30 → q = 15 cm · m = 15/30 = 0.5, real & inverted
Real world: concave → shaving & dentist mirrors, headlight reflectors; convex → vehicle rear-view mirrors ("objects are closer than they appear").
5 — Refraction & Snell's law
Crossing into a new medium light changes speed and bends. Into a denser medium it bends towards the normal; into a rarer one, away.
Snell's lawn = sin i / sin r = c / v
n(water) = 1.33 · n(glass) ≈ 1.5 · n(diamond) = 2.42
worked — refractive index
i = 45°, r = 28° in glass.
n = sin45°/sin28° = 0.707/0.469 = 1.51 · v = c/n = 1.99 × 10⁸ m/s
6 — Refractive index & apparent depth
Objects under water look raised: the swimming pool seems shallower, the coin in a glass floats up, the fish is deeper than it appears.
Apparent depthn = real depth / apparent depth
apparent = real / n → a water pool looks ¾ as deep
worked — the swimming pool
A pool is 2.0 m deep (n = 1.33).
apparent depth = 2.0/1.33 = 1.5 m — the floor looks half a metre higher than it is.
7 — Total internal reflection & critical angle
From denser to rarer, the refracted ray bends away from the normal. At the critical angle C it skims the surface (r = 90°); beyond C nothing escapes — total internal reflection.
Critical anglesin C = 1/n
glass → 41.8° · water → 48.8° · diamond → 24.4°
- Optical fibre — light trapped by repeated TIR carries your PTCL fibre internet and the surgeon's endoscope.
- Diamond fire — C is only 24.4°, so light is trapped and bounces many times before flashing out.
- Mirage — rays from the sky TIR off hot rare air above the road, which gleams like water.
8 — Lenses, lens formula & power
A convex lens converges, a concave lens diverges. The same formula as mirrors finds the image, and opticians grade lenses by power:
Lens formula & power1/f = 1/p + 1/q · m = q/p
P = 1/f(metres) → dioptre (D) · convex +, concave −
worked — projector setting
p = 30 cm, convex lens f = 20 cm.
1/q = 1/20 − 1/30 = 1/60 → q = 60 cm · m = 2 · P = 1/0.20 = +5 D
Object within f → virtual, erect, magnified image: the magnifying glass, with M = 1 + d/f (= 6× for f = 5 cm). A telescope is a long-focus objective plus a short-focus eyepiece: M = f₀/fₑ.
9 — The human eye & its defects
The cornea and lens form a real, inverted image on the retina; the ciliary muscles refocus the lens — accommodation. Normal vision: near point 25 cm to far point infinity.
| Defect | Image lands | Correcting lens |
|---|
| myopia (short sight) | before the retina | concave (P negative) |
| hypermetropia (long sight) | behind the retina | convex (P positive) |
worked — prescribing spectacles
A myopic eye sees clearly only to 2.0 m.
lens must image infinity at 2.0 m → f = −2.0 m → P = −0.5 D (concave)
10 — Worked numericals & exam recap
numerical — critical angle of diamond
n = 2.42.
sin C = 1/2.42 = 0.413 → C = 24.4° — why diamonds sparkle.
numerical — board practical f
p = 30.0 cm gives a sharp image at q = 21.4 cm.
f = pq/(p+q) = 642/51.4 = 12.5 cm
- Straight-line light → shadows, eclipses, pinhole camera.
- ∠i = ∠r from the normal; plane image virtual, q = p, laterally inverted.
- f = R/2; 1/f = 1/p + 1/q; m = q/p — mirrors and lenses alike.
- n = sin i / sin r = c/v; apparent depth = real/n.
- TIR when denser→rarer and i > C, sin C = 1/n — fibres, diamonds, mirage.
- P = 1/f(m) dioptres; myopia → concave, hypermetropia → convex.
- Magnifier M = 1 + d/f; telescope M = f₀/fₑ.